Controlling the crystal structure is a powerful approach for manipulating the fundamental properties of solids. Unique to two-dimensional (2D) van der Waals materials, the control can be achieved by modifying the stacking order through rotation and translation between the layers. Here, we report the first observation of stacking dependent interlayer magnetism in the 2D magnetic semiconductor, chromium tribromide (CrBr3), enabled by the successful growth of its monolayer and bilayer through molecular beam epitaxy. Using in situ spin-polarized scanning tunneling microscopy and spectroscopy, we directly correlated the atomic lattice structure with observed magnetic order. We demonstrated that while individual CrBr3 monolayer is ferromagnetic, the interlayer coupling in bilayer depends strongly on the stacking order and can be either ferromagnetic or antiferromagnetic. Our observations provide direct experimental evidence for exploring the stacking dependent layered magnetism, and pave the way for manipulating 2D magnetism with unique layer twist angle control.
Aiming to clarify the mechanisms governing the interlayer magnetic coupling, we have investigated the stacking energy and interlayer magnetism of bilayer CrBr$_3$ systemically. The magnetic ground states of bilayer CrBr$_3$ with different R-type and H-type stacking orders are established, which is found to be in good agreement with recent experiment (Science $\mathbf{366}$,983(2019)).Further analyses indicate that the stacking energy is mainly determined by the Coulomb interaction between the interlayer nearest-neighbor Br-Br atoms. While interlayer magnetism can be understood by a competition…
We address the interplay between stacking and interlayer exchange for ferromagnetically ordered CrI$_3$, both for bilayers and bulk. Whereas bulk CrI$_3$ is ferromagnetic, both magneto-optical and transport experiments show that interlayer exchange for CrI$_3$ bilayers is antiferromagnetic. Bulk CrI$_3$ is known to assume two crystal structures, rhombohedral and monoclinic, that differ mostly in the stacking between monolayers. Below 210-220 Kelvin, bulk CrI$_3$ orders in a rhombohedral phase. Our density functional theory calculations show a very strong dependence of interlayer exchange and s…
We develop a theory for interlayer tunneling in van der Waals heterostructures driven under a strong electromagnetic field, using graphene/{\it h}-BN/graphene as a paradigmatic example. Our theory predicts that strong anti-resonances appear at bias voltage values equal to an integer multiple of the light frequency. These features are found to originate from photon-assisted resonant tunneling transitions between Floquet sidebands of different graphene layers, and are unique to two-band systems due to the interplay of both intraband and interband tunneling transitions. Our results point to the p…
Long-lived interlayer excitons with distinct spin-valley physics in van der Waals heterostructures based on transition metal dichalcogenides make them promising for information processing in next-generation devices. While the emission characteristics of interlayer excitons in different types of hetero stacks have been extensively studied, the manipulation of these excitons required to alter the valley-state or tune the emission energy and intensity is still lacking. Here, we demonstrate such control over interlayer excitons in MoSe2/WSe2 heterostructures. The encapsulation of our stack with h-…
Throughout the years, strongly correlated coherent states of excitons have been the subject of intense theoretical and experimental studies. This topic has recently boomed due to new emerging quantum materials such as van der Waals (vdW) bound atomically thin layers of transition metal dichalcogenides (TMDs). We analyze the collective properties of charged interlayer excitons observed recently in bilayer TMD heterostructures. We predict new strongly correlated phases - crystal and Wigner crystal - that can be selectively realized with TMD bilayers of properly chosen electron-hole effective mas…
Exciton binding energies of hundreds of meV and strong light absorption in the optical frequency range make transition metal dichalcogenides (TMDs) promising for novel optoelectronic nanodevices. In particular, atomically thin TMDs can be stacked to heterostructures enabling the design of new materials with tailored properties. The strong Coulomb interaction gives rise to interlayer excitons, where electrons and holes are spatially separated in different layers. In this work, we reveal the microscopic processes behind the formation, thermalization and decay of these fundamentally interesting a…
We have investigated the vibrational properties of van der Waals heterostructures of monolayer transition metal dichalcogenides (TMDs), specifically MoS2/WSe2 and MoSe2/MoS2 heterobilayers as well as twisted MoS2 bilayers, by means of ultralow-frequency Raman spectroscopy. We discovered Raman features (at 30 ~ 40 cm-1) that arise from the layer-breathing mode (LBM) vibrations between the two incommensurate TMD monolayers in these structures. The LBM Raman intensity correlates strongly with the suppression of photoluminescence that arises from interlayer charge transfer. The LBM is generated on…
Van der Waals heterostructures constitute a platform for investigating intriguing many-body quantum phenomena. In particular, transition-metal dichalcogenide (TMD) hetero-bilayers host long-lived interlayer excitons which exhibit permanent out-of-plane dipole moments. Here, we develop a microscopic theory for interlayer exciton-exciton interactions including both the dipolar nature of interlayer excitons as well as their fermionic substructure, which gives rise to an attractive fermionic exchange. We find that these interactions contribute to a drift force resulting in highly non-linear excito…
Different atomistic registry between the layers forming the inner and outer nanotubes can form one-dimensional (1D) van der Waals (vdW) moiré superlattices. Unlike the two-dimensional (2D) vdW moiré superlattices, effects of 1D vdW moiré superlattices on electronic and optical properties in 1D moiré superlattices are not well understood, and they are often neglected. In this Perspective, we summarize new experimental observations and theoretical perspectives related to interlayer interactions in double-walled carbon nanotubes (DWNTs), a representative 1D vdW moiré system. Our discussion will f…
The experimental knowledge on interlayer potential of graphenites is summarized and compared with computational results based on phenomenological models. Besides Lennard-Jones approximation, the Mie potential is discussed, Kolmogorov-Crespy model and equation of Lebedeva et al. An agreement is found between a set of reported physical properties of graphite (compressibility along c-axis under broad pressure range, Raman frequencies for bulk shear and breathing modes under pressure, layer binding energies), when a proper choice of model parameters is made. It is argued that the Kolmogorov-Crespy…
We study the effect of perpendicular electric fields on the band structures of ABA and ABC graphene multilayers, and find that the electronic screening effect is significantly different between them. In ABA multilayers, the field produces a band overlap and gives a linear screening, while in ABC multilayers, in contrast, it opens an energy gap in the surface-state band at low energy, leading to a strong screening effect essentially non-linear to the field amplitude. The energy gap of a large ABC stack sharply rises when the external field exceeds a certain critical value.
Stacking order can significantly influence the physical properties of two-dimensional (2D) van der Waals materials. The recent isolation of atomically thin magnetic materials opens the door for control and design of magnetism via stacking order. Here we apply hydrostatic pressure up to 2 GPa to modify the stacking order in a prototype van der Waals magnetic insulator CrI3. We observe an irreversible interlayer antiferromagnetic (AF) to ferromagnetic (FM) transition in atomically thin CrI3 by magnetic circular dichroism and electron tunneling measurements. The effect is accompanied by a monocli…
In graphite crystals, layers of graphene reside in three equivalent, but distinct, stacking positions typically referred to as A, B, and C projections. The order in which the layers are stacked defines the electronic structure of the crystal, providing an exciting degree of freedom which can be exploited for designing graphitic materials with unusual properties including predicted high-temperature superconductivity and ferromagnetism. However, the lack of control of the stacking sequence limits most research to the stable ABA form of graphite. Here we demonstrate a strategy to control the stac…
With the help of the quantum chemistry methods we have investigated the nature of interlayer interactions between graphene fragments in different stacking arrangements (AA and AB). We found that the AB stacking pattern as the ground state of the system, is characterized by the effective inter-band orbital interactions which are barely present in the AA. Their vanishing induces electronic decoupling between the graphene layers, so that the bonding interaction $ΔE_{oi}$ between the flakes is drastically reduced from -0.482 eV to -0.087 eV as the stacking pattern is changed from AB to AA. The eff…
We study a family of globally smooth spatially varying two dimensional stacking textures in bilayer graphene. We find that the strain-minimizing stacking patterns connecting inequivalent ground states with local $AB$ and $BA$ interlayer registries are two dimensional twisted textures of an interlayer displacement field. We construct and display these topological stacking textures for bilayer graphene, examine their interactions and develop the composition rules that allow us to represent other more complex stacking textures, including globally twisted graphenes and extended one dimensional dom…
Due to their unique two-dimensional nature, charge carriers in semiconducting transition metal dichalcogenides (TMDs) exhibit strong unscreened Coulomb interactions and sensitivity to defects and impurities. The versatility of van der Waals layer stacking allows spatially separating electrons and holes between different TMD layers with staggered band structure, yielding interlayer few-body excitonic complexes whose nature is still debated. Here we combine quantum Monte Carlo calculations with spectrally and temporally resolved photoluminescence measurements on a top- and bottom-gated MoSe2/WSe…
Monolayer (ML) transition metal dichalcogenides (TMDs) integrated in optical microcavities host exciton-polaritons as a hallmark of the strong light-matter coupling regime. Analogous concepts for hybrid light-matter systems employing spatially indirect excitons with a permanent electric dipole moment in heterobilayer (HBL) crystals promise realizations of exciton-polariton gases and condensates with immanent dipolar interactions. Here, we identify optical signatures of spatially indirect momentum-bright and momentum-dark interlayer excitons in vertical MoSe$_2$-WSe$_2$ heterostructures and imp…
Controlling magnetism by purely electrical means is a key challenge to better information technology1. A variety of material systems, including ferromagnetic (FM) metals2,3,4, FM semiconductors5, multiferroics6,7,8 and magnetoelectric (ME) materials9,10, have been explored for the electric-field control of magnetism. The recent discovery of two-dimensional (2D) van der Waals magnets11,12 has opened a new door for the electrical control of magnetism at the nanometre scale through a van der Waals heterostructure device platform13. Here we demonstrate the control of magnetism in bilayer CrI3, an …
Diverse interlayer tunability of physical properties of two-dimensional layers mostly lies in the covalent-like quasi-bonding that is significant in electronic structures but rather weak for energetics. Such characteristics result in various stacking orders that are energetically comparable but may significantly differ in terms of electronic structures, e.g. magnetism. Inspired by several recent experiments showing interlayer anti-ferromagnetically coupled CrI3 bilayers, we carried out first-principles calculations for CrI3 bilayers. We found that the anti-ferromagnetic coupling results from a…
The interlayer interaction in graphene/boron-nitride heterostructures is studied using density functional theory calculations with the correction for van der Waals interactions. It is shown that the use of the experimental interlayer distance allows to describe the potential energy surface at the level of more accurate but expensive computational methods. On the other hand, it is also demonstrated that the dependence of the interlayer interaction energy on the relative in-plane position of the layers can be fitted with high accuracy by a simple expression determined by the system symmetry. The…
Stacking-dependent interlayer interactions are important for understanding the structural and electronic properties in incommensurable two dimensional material assemblies where long-range moiré patterns arise due to small lattice constant mismatch or twist angles. Here, we study the stacking-dependent interlayer coupling energies between graphene (G) and hexagonal boron nitride (BN) homo- and hetero-structures using high-level random-phase approximation (RPA) ab initio calculations. Our results show that although total binding energies within LDA and RPA differ substantially between a factor o…
Two-dimensional (2D) layered materials have been extensively studied owing to their fascinating and technologically relevant properties. Their functionalities can be often tailored by the interlayer stacking pattern. Low-frequency (LF) Raman spectroscopy provides a quick, non-destructive and inexpensive optical technique for stacking characterization, since the intensities of LF interlayer vibrational modes are sensitive to the details of the stacking. A simple and generalized interlayer bond polarizability model is proposed here to explain and predict how the LF Raman intensities depend on co…
We reveal stacking-induced strong coupling between atomic motion and interlayer excitons through photocurrent measurements of WSe$_2$/MoSe$_2$ heterojunction photodiodes. Strong coupling manifests as pronounced periodic sidebands in the photocurrent spectrum in frequency windows close to the interlayer exciton resonances. The sidebands, which repeat over large swathes of the interlayer exciton photocurrent spectrum, occur in energy increments corresponding directly to a prominent vibrational mode of the heterojunction. Such periodic patterns, together with interlayer photoconductance oscillati…
We have investigated the interlayer shear and breathing phonon modes in MoS$_{2}$ with pure 3R and 2H stacking order by using polarization-dependent ultralow-frequency Raman spectroscopy. We observe up to three shear branches and four breathing branches in MoS$_{2}$ with thickness from 2 to 13 layers. The breathing modes show the same Raman activity behavior for both polytypes, but the 2H breathing frequencies are consistently several wavenumbers higher than the 3R breathing frequencies, signifying that 2H MoS$_{2}$ has slightly stronger interlayer lattice coupling than 3R MoS$_{2}$. In contra…
Peeling, shearing, and sliding are important mechanical phenomena in van der Waals solids. However, theoretically they have been studied mostly using minimal periodic cells and in the context of accurate quantum simulations. Here, we investigate the peeling of large-scale multilayer graphene stacks with varying thicknesses, stackings, and peeling directions by using classical molecular dynamics simulations with a registry-dependent interlayer potential. Simulations show that, while at large scale the peeling proceeds smoothly, at small scale the registry shifts and sliding patterns of the laye…
The infrared absorption spectra of ABC-stacking tri- and tetra-layer graphenes are studied using the density functional theory. It is found that they exhibit very different characteristic peaks compared with those of AB-stacking ones, caused by the different stacking sequence and interlayer coupling. The anisotropy of the spectra with respect to the direction of the light electric field is significant. The spectra are more sensitive to the stacking number when the electric field is perpendicular to the graphene plane due to the interlayer polarization. The high sensitivities make it possible t…
Monolayers of transition metal dichalcogenides (TMDCs) feature exceptional optical properties that are dominated by excitons, tightly bound electron-hole pairs. Forming van der Waals heterostructures by deterministically stacking individual monolayers allows to tune various properties via choice of materials and relative orientation of the layers. In these structures, a new type of exciton emerges, where electron and hole are spatially separated. These interlayer excitons allow exploration of many-body quantum phenomena and are ideally suited for valleytronic applications. Mostly, a basic mode…
Van der Waals heterostructures, vertical stacks of layered materials, offer newopportunities for novel quantum phenomena which are absent in their constituent components. Here we report the emergence of polaron quasiparticles at the interface of graphene/hexagonal boron nitride (h-BN) heterostructures. Using nanospot angle-resolved photoemission spectroscopy, we observe zone-corner replicas of h-BN valence band maxima, with energy spacing coincident with the highest phonon energy of the heterostructure|an indication of Frohlich polaron formation due to forward scattering electron-phonon coupl…
Van der Waals heterostructures give access to a wide variety of new phenomena that emerge thanks to the combination of properties brought in by the constituent layered materials. We show here that owing to an enhanced interaction cross section with electrons in a type I van der Waals heterostructure, made of single layer molybdenum disulphide and thin boron nitride films, electrons and holes created in boron nitride can be transferred to the dichalcogenide where they form electron-hole pairs yielding luminescence. This cathodoluminescence can be mapped with a spatial resolution far exceeding w…
Using bilayer CrI$_3$ as an example, we demonstrate that stacking domain walls in van der Waals magnets can host one dimensional (1D) magnon channels, which have lower energies than bulk magnons. Interestingly, some magnon channels are hidden in magnetically homogeneous background and can only be inferred with the knowledge of stacking domain walls. Compared to 1D magnons confined in magnetic domain walls, 1D magnons in stacking domain walls are more stable against external perturbations. We show that the relaxed moiré superlattices of small-angle twisted bilayer CrI$_3$ is a natural realizati…
Atoms start behaving as waves rather than classical particles if confined in spaces commensurate with their de Broglie wavelength. At room temperature this length is only about one angstrom even for the lightest atom, hydrogen. This restricts quantum-confinement phenomena for atomic species to the realm of very low temperatures. Here we show that van der Waals gaps between atomic planes of layered crystals provide angstrom-size channels that make quantum confinement of protons apparent even at room temperature. Our transport measurements show that thermal protons experience a notably higher ba…
We have studied boron nitride monolayer and bilayer band structures. For bilayers, the ground state energies of the different five stackings are computed using DFT in order to determine the most stable configuration. Also, the interlayer distance for the five different types of stacking in which boron-nitride bilayers can be found is determined. Using a minimal tight binding model for the band structures of boron nitride bilayers, the hopping parameters and the onsite energies have been extracted by fitting a tight binding empirical model to the DFT results.
We investigate the ultralow-frequency Raman response of atomically thin ReS2, a special type of two-dimensional (2D) semiconductors with unique distorted 1T structure. Bilayer and few-layer ReS2 exhibit rich Raman spectra at frequencies below 50 cm-1, where a panoply of interlayer shear and breathing modes are observed. The emergence of these interlayer phonon modes indicate that the ReS2 layers are coupled and stacked orderly, in contrast to the general belief that the ReS2 layers are decoupled from one another. While the interlayer breathing modes can be described by a linear chain model as …
We study interlayer transport of multilayer graphenes in magnetic field with various stacking structures (AB, ABC, and AA types) by calculating the Hall and longitudinal conductivities as functions of Fermi energy. Their behavior depends strongly on the stacking structures and selection of the layers. The Hall conductivity between different layers is no longer quantized. Moreover, for AB stacking, the interlayer conductivity vanishes around zero energy with increasing layer separation, and shows negative values in particular cases. The fact that longitudinal interlayer conductivity suppressed …
Two-dimensional semiconductors feature valleytronics phenomena due to locking of the spin and momentum valley of the electrons. However, the valley polarization is intrinsically limited in monolayer crystals by the fast intervalley electron-hole exchange. Hetero-bilayer crystals have been shown to have a longer exciton lifetime and valley depolarization time. But the reported valley polarization was low; the valley selection rules and mechanisms of valley depolarization remains controversial. Here, we report singlet and brightened triplet interlayer excitons both with over 80% valley polarizat…
Stacked van der Waals (vdW) heterostructures where semi-conducting two-dimensional (2D) materials are contacted by overlayed graphene electrodes enable atomically-thin, flexible electronics. We use first-principles quantum transport simulations of graphene-contacted MoS2 devices to show how the transistor effect critically depends on the stacking configuration relative to the gate electrode. We can trace this behavior to the stacking-dependent response of the contact region to the capacitive electric field induced by the gate. The contact resistance is a central parameter and our observation e…
The weak interlayer coupling in van der Waals (vdW) magnets has confined their application to two dimensional (2D) spintronic devices. Here, we demonstrate that the interlayer coupling in a vdW magnet Fe$_3$GeTe$_2$ (FGT) can be largely modulated by a protonic gate.With the increase of the protons intercalated among vdW layers,interlayer magnetic coupling increases.Because of the existence of antiferromagnetic layers in FGT nanoflakes, the increasing interlayer magnetic coupling induces exchange bias in protonated FGT nanoflakes. Most strikingly, a rarely seen zero-field cooled (ZFC) exchange …
The intriguing physics of carrier-carrier interactions, which likewise affect the operation of light emitting devices, stimulate the research on semiconductor structures at high densities of excited carriers, a limit reachable at large pumping rates or in systems with long-lived electron-hole pairs. By electrically injecting carriers into WSe$_2$/MoS$_2$ type-II heterostructures which are indirect in real and k-space, we establish a large population of typical optically silent interlayer excitons. Here, we reveal their emission spectra and show that the emission energy is tunable by an applied…
Transition metal dichalcogenide heterostructures can host interlayer excitons (IXs), which consist of electrons and holes spatially separated in different layers. IXs possess permanent dipoles and have proven to offer a wealth of novel physics. We develop a discrete, random-walk model which includes annihilation and repulsion interactions among IXs. Using this model, we simulate the trapping of IXs in traps of different depths, densities, and shapes. Our results show that dipole-dipole interactions play an important role in regulating IX trapping. The effects of dipole interactions can be miti…
We directly measure the electronic structure of twisted graphene/MoS2 van der Waals heterostructures, in which both graphene and MoS2 are monolayers. We use cathode lens microscopy and microprobe angle-resolved photoemission spectroscopy measurements to image the surface, determine twist angle, and map the electronic structure of these artificial heterostructures. For monolayer graphene on monolayer MoS2, the resulting band structure reveals the absence of hybridization between the graphene and MoS2 electronic states. Further, the graphene-derived electronic structure in the heterostructures r…
We perform an optical spectroscopy study to investigate the properties of different artificial MoS$_2$ bi- and trilayer stacks created from individual monolayers by a deterministic transfer process. These twisted bi- and trilayers differ from the common 2H stacking in mineral MoS$_2$ in the relative stacking angle of adjacent layers and the interlayer distance. The combination of Raman spectroscopy, second-harmonic-generation microscopy and photoluminescence measurements allows us to determine the degree of interlayer coupling in our samples. We find that even for electronically decoupled arti…
We explore the skyrmion formation and control possibilities in 2D magnets from the ubiquitous moiré pattern in vdW heterostructures. Using the example of a ferromagnetic monolayer on an antiferromagnetic substrate, we demonstrate a new origin of skyrmions in the 2D magnets, from the lateral modulation of interlayer magnetic coupling by the locally different atomic registries in moiré. The moiré skyrmions are doubly degenerate with opposite topological charge, and trapped at an ordered array of sites with the moiré periodicity that can be dramatically tuned by strain and interlayer translation.…
The self-trapped state (STS) of interlayer exciton (IX) has been aroused enormous interesting owing to their significant impact on the fundamental properties of the van derWaals heterostructures (vdWHs). Nevertheless, the microscopic mechanisms of STS are still controversial. Herein, we study the corrections of the binding energies of the IXs due to the exciton-interface optical phonon coupling in four kinds of vdWHs and find that these IXs are in the STS for the appropriate ratio of the electron and hole effective masses. We show that these STSs could be classified into the type I with the in…
The interlayer coupling, which has a strong influence on the properties of van der Waals heterostructures, strongly depends on the interlayer distance. Although considerable theoretical interest has been demonstrated, experiments exploiting a variable interlayer coupling on nanocircuits are scarce due to the experimental difficulties. Here, we demonstrate a novel method to tune the interlayer coupling using hydrostatic pressure by incorporating van der Waals heterostructure based nanocircuits in piston-cylinder hydrostatic pressure cells with a dedicated sample holder design. This technique op…
Complex van der Waals heterostructures from layered molecular stacks are promising optoelectronic materials offering means to efficient, modular charge separation and collection layers. The effect of stacking in the electrodynamics of such hybrid organic-inorganic two-dimensional materials remains largely unexplored, whereby molecular scale engineering could lead to advanced optical phenomena. For instance, tunable Fano engineering could make possible on-demand transparent conducting layers or photoactive elements, and passive cooling. We employ an adapted Gersten-Nitzan model and real time ti…
A magnon spin-orbit coupling, induced by the dipole-dipole interaction, is derived in monoclinic-stacked bilayer honeycomb spin lattice with perpendicular magnetic anisotropy and antiferromagnetic interlayer coupling. Linear crossings are predicted in the magnon spectrum around the band minimum in G valley, as well as in the high frequency range around the zone boundary. The linear crossings in K and K' valleys, which connect the acoustic and optical bands, can be gapped when the intralayer dipole-dipole or Kitaev interactions exceed the interlayer dipole-dipole interaction, resulting in a pha…
In van der Waals heterostructures, the periodic potential from the Moiré superlattice can be used as a control knob to modulate the electronic structure of the constituent materials. Here we present a nanoscale angle-resolved photoemission spectroscopy (Nano-ARPES) study of transferred graphene/h-BN heterostructures with two different stacking angles of 2.4° and 4.3° respectively. Our measurements reveal six replicas of graphene Dirac cones at the superlattice Brillouin zone (SBZ) centers. The size of the SBZ and its relative rotation angle to the graphene BZ are in good agreement with Moiré s…
Combining atomically-thin van der Waals materials into heterostructures provides a powerful path towards the creation of designer electronic devices. The interaction strength between neighboring layers, most easily controlled through their interlayer separation, can have significant influence on the electronic properties of these composite materials. Here, we demonstrate unprecedented control over interlayer interactions by locally modifying the interlayer separation between graphene and boron nitride, which we achieve by applying pressure with a scanning tunneling microscopy tip. For the spec…
We show that anisotropic energy of a 2D antiferromagnet is greatly enhanced via stacking on a magnetic substrate layer, arising from the sublattice-dependent interlayer magnetic interaction that defines an effective anisotropic energy. Interestingly, this effective energy couples strongly with the interlayer stacking order and the magnetic order of the substrate layer, providing unique mechanical and magnetic means to control the antiferromagnetic order. These two types of control methods affect distinctly the sublattice magnetization dynamics, with a change of the ratio of sublattice precessi…
In van der Waals (vdW) heterostructures formed by stacking two monolayer semiconductors, lattice mismatch or rotational misalignment introduces an in-plane moiré superlattice. While it is widely recognized that a moiré superlattice can modulate the electronic band structure and lead to novel transport properties including unconventional superconductivity and insulating behavior driven by correlations, its influence on optical properties has not been investigated experimentally. We present spectroscopic evidence that interlayer excitons are confined by the moiré potential in a high-quality MoSe…
Exchange-correlation functionals with corrections for van der Waals interactions (PBE-D2, PBE-D3, PBE-D3(BJ), PBE-TS, optPBE-vdW and vdW-DF2) are tested for graphene and hexagonal boron nitride, both in the form of bulk and bilayer. The characteristics of the potential energy surface, such as the barrier to relative sliding of the layers and magnitude of corrugation, and physically measurable properties associated with relative in-plane and out-of-plane motion of the layers including the shear modulus and modulus for axial compression, shear mode frequency and frequency of out-of-plane vibrati…
The optical and electronic properties of van der Waals (vdW) heterostructures depend strongly on the atomic stacking order of the constituent layers. This is exemplified by periodic variation of the local atomic registry, known as moire patterns, giving rise to superconductivity and ferromagnetism in twisted bilayer graphene and novel exciton states in transition metal dichalcogenides (TMD) heterobilayers. However, the presence of the nanometer-scale moire superlattices is typically deduced indirectly, because conventional imaging techniques, such as transmission electron microscopy (TEM), req…
